Why Stress Test Really Means Guesswork

Well, we’ve heard a ton about stress tests recently. Want some details on what a stress test entails? The Journal has some details about the tests here. Now, as much as I think GDP and unemployment are fine things to project forward for economists, let’s walk through the way one would use this to actually price an asset. Let’s start with something simple, like a 10-year treasury note (note that treasury bond specifically refers to bonds with a 30-year maturity). Here are all the components one would need to stress test the value of a treasury note.

  1. Characteristics of the note itself: coupon, payment dates, maturity dates, etc.
  2. What the yield curve would look like at the date you’re pricing the note.

Why would one need to know the shape of the yield curve (term structure of rates)? This is important, in order to “PV” the bond’s cashflows most accurately, one would discount each cashflow by it’s risk–the simplest proxy is to discount each cash flow by the rate of interest one would need to pay to issue a bond maturing on that date. For the government, this rate of interest is the point on the treasury yield curve (actually, the par zero curve) with the same maturity date. An example would be, if I were going to price a cash payment I will receive in two years, and the government can currently issue two-year debt at 5%, I should discount my cash payment (also from the government, since it’s a treasury note) at 5%. Treasuries are the simplest of all instruments to value.

Here’s an example, form the link above, of what a treasury yield curve might look like:

Normal Yield Curve

Now, it is completely and totally guesswork to figure out, given unemployment and GDP figures, what the yield curve will look like at any date in the future. Indeed, one can plug these projections into a model and it can come up with a statistical guess… But the only thing we know for sure about that guess is that it won’t be accurate, although it might be close. However, things like inflation will drive the longer end of the yield curve and monetary policy will drive the shorter end, so these certainly aren’t directly taken from the stress test parameters, but would need to be a guess based on those parameters. This is a large source of uncertainty in pricing even these instruments in the stress test.

Next, let’s examine a corporate bond. What would we need for a corporate bond?

  1. Characteristics of the bond: coupon, payment dates, maturity dates, special features (coupon steps, sinking funds, call schedules, etc.), where in the capital structure this bond sits, etc.
  2. What the yield curve would look like at the date you’re pricing the bond.
  3. The spreads that the corporation’s debt will carry at the date you’re pricing the bond.

Oh no. We already saw the issues with #2, but now we have #3. What will this corporations credit spread (interest/yield required in excess of the risk free rate) at the time of pricing? Will the corporations debt, which could trade at a spread of anywhere from 5 to 1500 basis points, be lower? higher? Will the corporations spread curve be flatter? steeper?

Here is a good illustration of what I’m referring to (from the same source as the figure above):

Credit Spread

There, the spread is the difference between the purple line and the black line. As you can see, it’s different for different maturity corporate bonds (which makes sense, because if a company defaults in year two, it’ll also default on it’s three year debt.. but the companies’ two year debt might never default, but the company might default during it’s third year, creating more risk for three year bonds issued by that company than two year bonds). It shouldn’t be a surprise, after our exercise above, to learn that the best way to compute the price of a corporate bond is to discount each cashflow by it’s risk (in my example above, regardless of whether the company defaults in year two or year three, the interest payments from both the three year and two year debt that are paid in one year have the same risk).

Well, how does one predict the structure of credit spreads in the future? Here’s a hint: models. Interest rates, however, are an input to this model, since the cost of a firm’s borrowing is an important input to figuring out a corporation’s cashflow and, by extension, creditworthiness. So now we have not only a flawed interest rate projection, but we have a projection of corporate risk that, in addition to being flawed itself, takes our other flawed projections as an input! Understanding model error yet? Oh, and yes unemployment and the health of the economy will be inputs to the model that spits out our guess for credit spreads in the future as well.

Next stop on the crazy train, mortgage products! What does one need to project prices for mortgage products?

  1. Characteristics of the bond: coupon, payment dates, maturity dates, structure of the underlying securitization (how does cash get assigned in the event of a default, prepayment, etc.), etc.
  2. What the yield curve would look like at the date you’re pricing the bond.
  3. The spreads that the debt will carry at the date you’re pricing the bond.
  4. What prepayments will have occurred by the date you’re pricing the bond and what prepayments will occur in the future, including when each will occur.
  5. What defaults will have occurred by the date you’re pricing the bond and what defaults will occur in the future, including when each will occur.

Oh crap. We’ve covered #1-3. But, look at #4 and #5 … To price a mortgage bond, one needs to be able to project out, over the life of the bond, prepayments and defaults. Each is driven bydifferent variables and each happens in different timeframes. Guess how each projection is arrived at? Models! What are the inputs to these models? Well, interest rates (ones ability to refinance depends on where rates are at the time) over a long period of time (keep in mind that you need rates over time, having rates at 5% in three years is completely different if rates where 1% or 15% for the three years before). General economic health, including regional (or more local) unemployment rates (if the south has a spike in unemployment, but the rest of the country sees a slight decrease, you’ll likely see defaults increase). And a myrid of other variables can be tossed in for good measure. So now we have two more models, driven by our flawed interest rate projections, flawed credit projections (ones ability to refinance is driven by their mortgage rate, which is some benchmark interest rate [treasuries here] plus some spread, from #3), and the unemployment and GDP projections.

I will, at this point, decline to talk about pricing C.D.O.’s … Just understand, however, that C.D.O.’s are portfolios of corporate and mortgage bonds, so they are a full extra order of magnitude more complex. Is it clear, now, why these stress tests, as they seem to be defined, aren’t all that specific, and potentially not all that useful?

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